Gerbes and Duality
Abstract
We describe a global approach to the study of duality transformations between antisymmetric fields with transitions and argue that the natural geometrical setting for the approach is that of gerbes; these objects are mathematical constructions generalizing U(1) bundles and are similarly classified by quantized charges. We address the duality maps in terms of the potentials rather than on their field strengths and show the quantum equivalence between dual theories which in turn allows a rigorous proof of a generalized Dirac quantization condition on the couplings. Our approach needs the introduction of an auxiliary form satisfying a global constraint which in the case of 1form potentials coincides with the quantization of the magnetic flux. We apply our global approach to refine the proof of the duality equivalence between the d=11 supermembrane and d=10 IIA Dirichlet supermembrane.
 Publication:

Annals of Physics
 Pub Date:
 August 2002
 DOI:
 10.1006/aphy.2002.6283
 arXiv:
 arXiv:hepth/0205002
 Bibcode:
 2002AnPhy.300...32C
 Keywords:

 High Energy Physics  Theory
 EPrint:
 47 pages, 1 figure, 2 references added